$\theta$ and the $\eta^\prime$ in Large $N$ Supersymmetric QCD

We study the large $N$ $\theta$ dependence and the $\eta^\prime$ potential in supersymmetric QCD with small soft SUSY-breaking terms. Known exact results in SUSY QCD are found to reflect a variety of expectations from large $N$ perturbation theory, including the presence of branches and the behavior of theories with matter (both with $N_f \ll N$ and $N_f \sim N$). However, there are also striking departures from ordinary QCD and the conventional large $N$ description: instanton effects, when under control, are not exponentially suppressed at large $N$, and branched structure in supersymmetric QCD is always associated with approximate discrete symmetries. We suggest that these differences motivate further study of large $N$ QCD on the lattice.